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Proof by mathematical Induction

courtneybcca

courtneybcca

New member
Anyone good at math... I need help with these kind of proves.... to be exact this question I am having trouble with I know how to get to the answer but I dont know how to prove it...

a+b is a factor of a^(2n+1) + b^(2n+1)
okay so a+b is a factor because (a+b)(a^(2) +2ab +b^(2))
the answer is a^(2k+3) = b^(2K+3)

But how do you get there.... Help. I just see the answer I dont know how to show the steps. My final is tomorrow...
 
What better place to turn to math help then a fitness board?

The question is funny. The better question is what are you going to do with that knowledge once you leave college.
 
Both good questions... I have read that we have some professionals with graduate degrees on here so I thought this would be a easily answered question for those people. I am desperate at this point I have been looking online and though my textbook and can’t figure it out…
I have no idea what I will need this for… But they make us learn it.
 
EnderJE said:
What better place to turn to math help then a fitness board?

The question is funny. The better question is what are you going to do with that knowledge once you leave college.
Click to expand...

he is expanding his brain. And for that matter he ulitmately seeks it among body builders. Even people with knowledge would cease to answer that. we flex different muscles here orb.
 
I still remember school and remember all the crap that they made us learn. Sheesh. 1+1=2. What a waste of time!
 
sorry to hijack your post sweetie, but has anyone here used a variable in any
math that they done since they were in school. To all you engineers out there, no need to reply to this.........we know you're smart, no need to rub it in our faces. ;)
 
I am glad everyone is having fun with this... Yes everything you learn in school is pretty much useless. But we all go through it. I don't care how you jack this thread but it would be really nice if someone would at least try to help. I will provide kisses and hugs..J/J
 
Apexx said:
sorry to hijack your post sweetie, but has anyone here used a variable in any
math that they done since they were in school. To all you engineers out there, no need to reply to this.........we know you're smart, no need to rub it in our faces. ;)
Click to expand...
yes, i use weird half remembered formulii and first principles all the time.

courtney, could you type out the full question properly? i dont know what youre trying to prove. i remember doing problems like this...just a long time ago
 
Okay this is the question I used ^for power like on a graphing calulator because there are no keys to square things etc...

Use mathematical induction to prove that a+b is a factor of a^(2n+1) + b^(2n+1)
 
sorry about the hijacking. I'm gonna go watch Good Will Hunting real quick to see if I can figure this out for ya. ;)

Untill I get back, bump for the engineers. Someone help the lovely young lady out.
 
to solve the question to replace n with (k+1) which gives you
a^(2(k+1) +1) +b^(2(k+1)) which equals a^(2k+3) + b^(2k+3)
but I have to prove the answer I dont know how to do that
 
Courtneybcca said:
Okay this is the question I used ^for power like on a graphing calulator because there are no keys to square things etc...

Use mathematical induction to prove that a+b is a factor of a^(2n+1) + b^(2n+1)
Click to expand...

Hmm, well, if n=0, then the equation is just a^(2(0)+1) + b^(2(0)+1) which is simply a^1 + b^1 or a + b. Therefore for any value of n a+b is going to be a factor. Such as with n=1 a^3 + b^3, and a=2 and b=1, the answer would be 8 + 1 and 3 (or a+b) is a factor of 9. So regardless of the value of n, a+b will be a factor since it holds true for n=0 or n=1 and so on. I'm not sure of exact procedure you need, but typically you start with the most simple cases and prove that each one holds true.
 
Courtneybcca said:
to solve the question to replace n with (k+1) which gives you
a^(2(k+1) +1) +b^(2(k+1)) which equals a^(2k+3) + b^(2k+3)
but I have to prove the answer I dont know how to do that
Click to expand...

Right, because you start with say n=0, prove it holds. and then n=k, so next try 1, or k+1, and prove it holds. Therefore for any k+1 it holds.
 
slickdadd said:
Hmm, well, if n=0, then the equation is just a^(2(0)+1) + b^(2(0)+1) which is simply a^1 + b^1 or a + b. Therefore for any value of n a+b is going to be a factor. Such as with n=1 a^3 + b^3, and a=2 and b=1, the answer would be 8 + 1 and 3 (or a+b) is a factor of 9. So regardless of the value of n, a+b will be a factor since it holds true for n=0 or n=1 and so on. I'm not sure of exact procedure you need, but typically you start with the most simple cases and prove that each one holds true.
Click to expand...
all that will do is prove that it holds true for the substituted values of k and n. it will not prove that the rule holds along the entire domain for the equation.

courtney, its familiar and forgotten to me, if i were you, go to sleep, and ask someone right before your test. no need to lose sleep and other revision time for something that you just need to be shown how to do.

cheers
 
OK now I better get pics for this but to prove by induction you assume that the proposition is true for the nth case and prove it is true for n = n + 1.
Then show it is true for a single case , say n = 0
Then state that since we have proved if it is true for n then it is true for n = n + 1 and we have shown it is true for n = 0 (say) then it follows that it must be true for all n.
QED
Easy

Proof for first part:
Assume general case for n i.e. (a+b) is a factor for (a^(2n+1) + b^(2n+1))
Then to prove that (a+b) is a factor for n+1 case i.e. (a^(2(n+1)+1) + b^(2(n+1)+1)

Now factorise (a^(2(n+1)+1) + b^(2(n+1)+1) :
(a +b) ((a^(2(n+1) + b^(2(n+1))) - ab^2n+2 - (a^2n+2) b
Therefore we only need to show that (ab^2n+2 + (a^2n+2) b) is factored by (a +b)
Ok so ab^2n+2 + (a^2n+2) b = ab (b^2n+1 + a^2n+1)
and since we know that b^2n+1 + a^2n+1 is factored by (a+b) from our assumption we are home free!
QED
 
Last edited:
OH okay I understand THANK YOU
we went over that in class but when I did the homework I just wrote down the answer but didn't prove it
THANK YOU THANK YOU
you want pics tell me where to send them
 
Okay you lost me now.... I went back and looked at your edited message... I have to write it out and look at it. It is hard to read this way
 
Courtneybcca said:
Okay you lost me now.... I went back and looked at your edited message... I have to write it out and look at it. It is hard to read this way
Click to expand...
Formatting available here is shit...Im sorry I dont have equation editor at work but if you take a good look at it , it will make sense.
First take the n+1 case - try and factorise it - then we try and factorise the remainder - when we take out the (a+b) term lo and behold we are left with the same term which we ASSUMED was true (the n case). That's it. Good luck.
 
it's a shame that any college curriculum would require that sweet ass of yours to have anything to do with mathematical induction.

that's less time for you to grind up against a pole.
 
So unfair that I missed this thread yesterday and earlier today!!

I'm a Mechanical Engineer......without pics or timing to say the least.
 
I don’t grind up against a pole thank you..... I am actually working on a bachelor degree in human biology and hopefully going to medical school. I work hard and am proud of my body.
 
Okay since we have some people awake now maybe you can help me with this one.... For each of the following, indicate if stronger intermolecular forces will make them increase, decrease or have no effect.
a. boiling point
b. melting point
c. vapor pressure
d. density
e. viscosity

Also when calculating the ph for .500M NH4 (little four) Ka = 5.6X 10^(-10)
do I have to set up a balanced equation first or just go straight to logs.
 
The answer is infinity

Ok, no its not

Whats my consolation prize?
 
ummm... nothing for now... I think I am going to keep this going whenever I need help with my school work. But no one has helped with the last one yet
 
Boy that question is making me feel stupid! I havent even needed to look into chem since school. I'm going to hit the books.
 
Courtneybcca said:
and hopefully going to medical school.
Click to expand...

You're in college? No offence, but you have no chance of getting into medical school with the questions you're asking us. Many competitive high school students are finished with or most of the way through organic chemistry and multivariable calculus by the time they graduate.



Courtneybcca said:
I have no idea what I will need this for… But they make us learn it.
Click to expand...

Wait 'till orgo.
 
Courtneybcca said:
Okay since we have some people awake now maybe you can help me with this one.... For each of the following, indicate if stronger intermolecular forces will make them increase, decrease or have no effect.
a. boiling point
b. melting point
c. vapor pressure
d. density
e. viscosity

Also when calculating the ph for .500M NH4 (little four) Ka = 5.6X 10^(-10)
do I have to set up a balanced equation first or just go straight to logs.
Click to expand...

OK first up im not certain of all of these since I have not touched chemistry in the last 4 years but as a damn good guess I'd say it's increase for all of them.

Second one - You need to calculate the extent to which the solution dissacciates into its hydrogen ion concentration. NH4 is a single proton donor - that's as far as I'm willing to help you unless you are really badly stuck - you wont get anywhere with someone just spoonfeeding you the answers - as well as that it will be more fun for you when you can get the right answer yourself. Good luck.

Finally Samoth please remember that genius is 99% perspiration - anyone trying to better themselves should be encouraged and not put down. No disrespect my man.
 
I'd like the pics too!



I'll help with future assignments ;)
 
Last edited by a moderator:
Mandinka2 said:
Finally Samoth please remember that genius is 99% perspiration - anyone trying to better themselves should be encouraged and not put down. No disrespect my man.
Click to expand...

But you need to remember that at the university level... especially with something as competitive as medical school... is that nobody cares how hard you try. They really couldn't care less. The adcomms only care about what is on your application: grades, recs, EC's, strength of curriculum, and prestige of past academic institutions.

Now, if you try hard at something and succeed , then you'll be looked upon favorably. But if you fail... well, welcome to life.

Anyone who has gone through university has undoubtedly run across dozens upon dozens of people that were pre-med. Most, if not all of them, fail (school prestige being a primary factor). Whether it was because the courses were too demanding, or the GPA requirements were too high, or the person actually wanted to have a social life... generally speaking, I honestly don't think most college freshmen truly understand what it takes.
 
Well thank you for the help guys I figured out the answer. Boiling point, melting point and viscosity increases. The density does not change. The Vapor pressure deceases.

The other one I knew just being stupid for a moment. NH4 combines with water because it is aqueous the produces H30+ and NH3 I had a blond moment for a second…

Thanks though…I could explain all that but I am sure none of you care. So as of today 4 finals down and one more to go…

Mr. Samoth
Thank you for encouraging me. That is always greatly appreciated. I have actually been working within the medical field I am pursuing for many years now. The field I am going into they need students because everyone is retiring. I have a lot of experience I just need the education. My grade point average is 3.8, I am an elected senator at my school, and I am part of the chemistry and pre-med clubs. I also belong to two honors societies. Plus I do volunteer work. To get into medical school you need grades of course but they want to see you in leadership positions and being involved in the community. I also have many reference letters from my teachers.
 
Courtneybcca said:
The field I am going into they need students because everyone is retiring. I have a lot of experience I just need the education.
Click to expand...
Curious now. What position? Why?
 
Courtneybcca said:
hmm if I tell you... You are going to think I am weird.... well I am sure you already do...
Click to expand...
I'm the one calling you BBF and you're worried that I think you're wierd? So, what is it?
 
Courtneybcca said:
Okay well there is a really long story behind this... Forensic Pathology...
Click to expand...
Wow. I wanted that career ALONG time ago. Kudos to you for picking it up. What's the Coles Notes version of the story? Lost a loved one to a crime or something?
 
Really? Wow…. It is funny I told people like 5 years ago that and they looked at me weird. Nowadays people are all over because of all the tv shows etc…

Okay coles notes.

-Wanted to be a doctor
-Friend becoming mortician
-Saw dead person
-Realized I am too afraid to kill someone
-Volunteered for coroner’s office
-Watched an autopsy
-etc
 
Courtneybcca said:
Really? Wow?. It is funny I told people like 5 years ago that and they looked at me weird. Nowadays people are all over because of all the tv shows etc?

Okay coles notes.

-Wanted to be a doctor
-Friend becoming mortician
-Saw dead person
-Realized I am too afraid to kill someone
-Volunteered for coroner?s office
-Watched an autopsy
-etc
Click to expand...
Neat stuff. When I was younger, I wanted to make a "difference" and fight crimes. The job of Superman was taken, so I thought I would try something like Sherlock Holmes and use my deductive reasoning to solve crimes. I started looking into autopsies and balistics.

I didn't get the marks I needed to get into science for it, so I started looking around at other opportunities to "make a difference".

Then, sadly, I saw how much these people were paid and basically said "fuck that" to join corporate canada.
 
Courtneybcca said:
Really? Wow?. It is funny I told people like 5 years ago that and they looked at me weird. Nowadays people are all over because of all the tv shows etc?

Okay coles notes.

-Wanted to be a doctor
-Friend becoming mortician
-Saw dead person
-Realized I am too afraid to kill someone
-Volunteered for coroner?s office
-Watched an autopsy
-etc
Click to expand...
You can be the red-head in CSI...sexy...
 
ha ha yeah it is really sad that I am going to go to school for like 13 years and possibly never be able to pay back my student loans. But I would rather do a job I love. Life is too short. The human body is the most interesting thing on this planet. The way that we die is in direct reflection to the way we lived this life. It is a honor to be able to tell peoples stories for them.
 
Courtneybcca said:
I have actually been working within the medical field I am pursuing for many years now. The field I am going into they need students because everyone is retiring. I have a lot of experience I just need the education. My grade point average is 3.8, I am an elected senator at my school, and I am part of the chemistry and pre-med clubs. I also belong to two honors societies. Plus I do volunteer work. To get into medical school you need grades of course but they want to see you in leadership positions and being involved in the community. I also have many reference letters from my teachers.
Click to expand...

Those are stats that will put you on par with those applying for med school. You said you have been working in your field of interest for "many years now"... I take that to imply that you are a non-traditional student? I have honestly never come across that, as people I have known or went to school with had their dreams crushed quite early (state public; quite common... not exactly a HYP). It's not really that they weren't capable... it's that they wanted a more of a 'typical' college life... and that doesn't mesh with grandiose dreams of a top ten med school.

While the adcomms do want to see excellent ECs and refs, it is the commitment to excelling academically that is almost always the downfall of students. Having three pages of ECs and a 3.0 GPA won't do much to help one get into medical school unless your a URM or a national award winner. ECs are more of a deciding factor for more prestigious schools or the Ivys or HYPSCM... but at that level, students are expected to have near perfect scores by default.
 
No I am not the traditional student. I took some time off to make sure this was really what I wanted to do. I have done a lot of work within the field, and for different branches of it. I investigated different avenues and decided to go this route. I don’t care if I go to a top ten med school. When I get ready to apply I will apply EVERYWHERE!! Across the US, Canada I will go abroad if need be. I will go to whatever school will take me. I have enough experience I just need to have the education I can get my foot in the door to get the job.
 
Courtneybcca said:
Okay since we have some people awake now maybe you can help me with this one.... For each of the following, indicate if stronger intermolecular forces will make them increase, decrease or have no effect.
a. boiling point
b. melting point
c. vapor pressure
d. density
e. viscosity

Also when calculating the ph for .500M NH4 (little four) Ka = 5.6X 10^(-10)
do I have to set up a balanced equation first or just go straight to logs.
Click to expand...
a- up - its harder to separate the molecules
b- up - same thing
c- down - molecules wont push away from each other as much
d- increase, since molecules will pack together more tightly
e- ooooo thats a funny one, youd have to assume that a colloid will not be affected, and all that...for the most part, viscocity should increase

and i hate logs, do it yourself :D
 
Courtneybcca said:
No I am not the traditional student. I took some time off to make sure this was really what I wanted to do. I have done a lot of work within the field, and for different branches of it. I investigated different avenues and decided to go this route. I don?t care if I go to a top ten med school. When I get ready to apply I will apply EVERYWHERE!! Across the US, Canada I will go abroad if need be. I will go to whatever school will take me. I have enough experience I just need to have the education I can get my foot in the door to get the job.
Click to expand...
Have you tried stripping? Its no pathology science, but the pay is nice. Just tell me where you are playing...

...kidding! Well, unless you really do it. :)
 
No I don't strip I have had plenty of offers for it but I think what I have already done is bad enough. I don't want anything to be brought up as a creditability issue when I am on the stand pleading cases. Plus my DREAM job would to be to work for the FBI in forensic investigations. But we will see about that.

Well I just finished my last exam and I totally aced it… YEAH!!! My boyfriend leaves for 3 weeks tomorrow and after Sunday I have nothing to do until January 3. I am going out with the girls Friday night.... I can’t wait!!! So I have only peace and quite to worry about and maybe some alcohol. Hee hee
 
Courtneybcca said:
No I don't strip I have had plenty of offers for it but I think what I have already done is bad enough. I don't want anything to be brought up as a creditability issue when I am on the stand pleading cases. Plus my DREAM job would to be to work for the FBI in forensic investigations. But we will see about that.

Well I just finished my last exam and I totally aced it… YEAH!!! My boyfriend leaves for 3 weeks tomorrow and after Sunday I have nothing to do until January 3. I am going out with the girls Friday night.... I can’t wait!!! So I have only peace and quite to worry about and maybe some alcohol. Hee hee
Click to expand...
Can i get the pics??
 
Courtneybcca said:
No I don't strip I have had plenty of offers for it but I think what I have already done is bad enough. I don't want anything to be brought up as a creditability issue when I am on the stand pleading cases. Plus my DREAM job would to be to work for the FBI in forensic investigations. But we will see about that.

Well I just finished my last exam and I totally aced it? YEAH!!! My boyfriend leaves for 3 weeks tomorrow and after Sunday I have nothing to do until January 3. I am going out with the girls Friday night.... I can?t wait!!! So I have only peace and quite to worry about and maybe some alcohol. Hee hee
Click to expand...
That would be funny. You could be CB...the stripping detective. I smell a sitcom!

Boyfriend leaving huh? Hmmm. Time for you to post pics!
 
Okay well I am not showing anyone else anymore pictures unless you help me in some way OR... you send me a picture first I have one on my profile and that is good enough for now.
 
Courtneybcca said:
Okay coles notes.

-Wanted to be a doctor
-Friend becoming mortician
-Saw dead person
-Realized I am too afraid to kill someone
-Volunteered for coroner’s office
-Watched an autopsy
-etc
Click to expand...

WTF :worried:

.....freak
 
Courtneybcca said:
Okay well I am not showing anyone else anymore pictures unless you help me in some way OR... you send me a picture first I have one on my profile and that is good enough for now.
Click to expand...
Okay, what help do you need?
 
samoth said:
But you need to remember that at the university level... especially with something as competitive as medical school... is that nobody cares how hard you try. They really couldn't care less. The adcomms only care about what is on your application: grades, recs, EC's, strength of curriculum, and prestige of past academic institutions.

Now, if you try hard at something and succeed , then you'll be looked upon favorably. But if you fail... well, welcome to life.

Anyone who has gone through university has undoubtedly run across dozens upon dozens of people that were pre-med. Most, if not all of them, fail (school prestige being a primary factor). Whether it was because the courses were too demanding, or the GPA requirements were too high, or the person actually wanted to have a social life... generally speaking, I honestly don't think most college freshmen truly understand what it takes.
Click to expand...

very true. Very good point.

I'm disappointed! I thought this thread was going to be strictly about mathematics. Proof by induction is one of the easiest methods of proof. Take cases for 0 , 1 , n and (n+1). It's very mechanical and gratifying.

Courtney if you need any more legitimate help with your math, you can ask me. For physics, don't even ask me.

And for your question about the logs, you can approach the problem using both methods. The steps are easy.
 
Courtneybcca said:
Okay well I am not showing anyone else anymore pictures unless you help me in some way OR... you send me a picture first I have one on my profile and that is good enough for now.
Click to expand...
I'll send you mine first.... what is your email?
 
Kroliczek said:
very true. Very good point.

I'm disappointed! I thought this thread was going to be strictly about mathematics. Proof by induction is one of the easiest methods of proof. Take cases for 0 , 1 , n and (n+1). It's very mechanical and gratifying.

Courtney if you need any more legitimate help with your math, you can ask me. For physics, don't even ask me.

And for your question about the logs, you can approach the problem using both methods. The steps are easy.
Click to expand...


You're such a nerd. :chomp:

If Kroli gets pics so should I
 
my roommate is going to be graduating with a BS in engineering math and BS in mathematics this spring, he'd know what to do.

I am in school for BS mechanical engineering.
 
people read back I already figured out the question but thank you for all the help. PM me for email I am not posting that. Thank goodness this semester is over!! Thanks for offering to help later. I am sure I will need it
 
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